Graphs of inequalities
Plotting graphs of inequalities works almost exactly the same way as plotting graphs.
Simple inequality graphs can be plotted parallel to the \(x\) or \(y\) axes and tables of values can help to plot more complex lines.
For example, this graph shows the inequality \(x \textless -1\). This can be seen as there is a dashed line at -1, and the A region is an area of the plane defined by one or more inequalities. that is less than this is shaded.
Example
Show the region satisfied by the inequality \(-2 \textless x \leq 3\).
Identify the regions shown by the inequalities. These are \(x \textgreater -2\) and \(x \leq 3\).
\(x \textgreater -2\) so draw a dotted line at \(x = -2\). \(x = -2\) is the graph made by coordinates points where \(x\) is equal to -2, for example (-2, 5), (-2, 4), (-2, 3), (-2, 2) and so on.
\(x \leq 3\) so draw a solid line at \(x = 3\). \(x = 3\) is the graph made by coordinate points where \(x\) is equal to 3, for example (3, -4), (3, -3), (3,-2), (3, -1) and so on.
The region which satisfies the inequalities is between these lines, so you need to highlight this section.
Question
Show the region of points satisfied by the inequalities \(-4 \leq y \textless 0\) and \(y \geq x\).
Identify the regions shown by the inequalities. These are \(y \geq -4\), \(y \textless 0\) and \(y \geq x\).
\(y \geq -4\) is a solid line at \(y = -4\). This line is made by the coordinate points where \(y = -4\), for example (5, -4) or (-5, -4). \(y\) is greater than or equal to this line, so shade the points above the line.
\(y \textless 0\) is a dashed line at \(y = 0\). This line is also known as the \(x\)-axis, as it is the line that goes through all the coordinate points where \(y = 0\). \(y\) is less than this line, so shade all the points below this line.
\(y \geq x\) is a solid line at \(y = x\). To draw the line \(y = x\), plot coordinate points where the \(y\) coordinate is equal to the \(x\) coordinate, for example (4, 4), (2, 2), (-1, -1) and so on. \(y\) is greater or equal to this line, so shade the region above this line.
The answer is the shaded region that matches all three inequalities.
More guides on this topic
- Equations of lines – WJEC
- Equations of curves - Intermediate & Higher tier – WJEC
- Basic algebra – WJEC
- Equations and formulae – WJEC
- Factorising - Intermediate & Higher tier – WJEC
- Quadratic expressions - Intermediate & Higher tier – WJEC
- Sequences – WJEC
- Functions - Higher only – WJEC
- Simultaneous equations - Intermediate & Higher tier – WJEC
